MAS252 Further Civil Engineering Mathematics and Computing
|Semester 1, 2021/22||10 Credits|
|Lecturer:||Dr Istvan Ballai||Timetable||Reading List|
Prerequisites: MAS151 (Civil Engineering Mathematics)
No other modules have this module as a prerequisite.
- Non-linear equations Netwon-Raphson method, bisection method.
- Ordinary differential equations Taylor series solution, Runge-Kutta methods for initial value problems, numerical solution of boundary value problems.
- Partial differentiation First and second derivatives, use of chain rule.
- Fourier Series Full range series, sine series, cosine series.
- Partial differential equations Classification, parabolic equations, Fourier series solution, numerical solution, Elliptical equations, Fourier series solutions, numerical solution.
- Analytical solutions (by separation of variables) of the ideal and non-ideal wave equation
- To consolidate and extend the understanding and use of various analytical and numerical techniques in the area of non-linear algebraic equations, Fourier series and partial differential equations.
- Solve non-linear algebraic equations by Newton-Raphson and bisection;
- Use Runge-Kutta methods to solve first and second order differential equations;
- Obtain partial derivatives of a function of two variables and use the chain rule;
- Expand functions in Fourier series;
- Solve the heat-conduction equation in one space-variable using explicit schemes;
- Solve simple parabolic partial differential equations using explicit schemes;
- Solve the Laplace equation in (x,y) by Fourier series;
- Solve linear elliptic partial differential equations in (x,y) by numerical methods.
- Solve linear hyperbolic differential equations (the wave equation) using analytical methods
Lectures, tutorials, problem solving
24 lectures, 12 tutorials
One formal 2 hour exam. [80%]
Matlab computer assessment exercise (taught by Civil Engineering Department) counts as 20% of the final mark.
|A||Stephenson||Mathematical Methods for Science Students||510 (S)||Blackwells||Amazon|
|A||Stroud||Engineering Mathematics||510.2462 (S)||Blackwells||Amazon|
|A||Stroud||Further Engineering Mathematics||510.2462 (S)||Blackwells||Amazon|
|C||Pivato||Linear Partial Differential Equations and Fourier Theory||Blackwells||Amazon|
(A = essential, B = recommended, C = background.)
Most books on reading lists should also be available from the Blackwells shop at Jessop West.